My boss (and, actually, his boss too, which is the company general director) are generally quite good.
But it happens (seldom, but frequently enough) that they start to fiddle with the details: day to day chores that they should not do.

Examples are: DB queries to extract data, scripts to parse excel files, even re-installing software on their workstation, and the like. The problem is that there are people in the company that could do it much better, much faster. Often, we already have programs or libraries to do what they are trying to do in a more efficient way, or we can create them.

This is not a very urgent problem, per-se (even if they make mistakes - not being their primary job, they may miss or forget important points), but that eats up their time, and that's the real issue: he does have very little time to "manage" (listen to his subordinates, make decisions, planning...)

How can I convince them to stop "doing", without being rude, annoying, or worse?
(he is still my boss, after all :) )
I know that for some people giving up the "getting my hands dirty" is difficult, but I really feel this is becoming a problem and I want to try to improve the situation.

EDIT:
Just to clarify: him doing things is both a problem by itself (but that is specific to my case, so I won't bother you with this part), and above all, a problem because it hinders his ability to manage others. Getting an answer by email is very difficult, meet him 1-1 to discuss projects, software to buy, planning, requires days or weeks, etc.

I am a team leader myself, and I strongly believe in leading by example, which means also working with your colleagues, but my first obligation with my people is to lead them, otherwise I may end up blocking 10 developers because they are waiting for an answer from me.

Sometimes I find myself doing small and simple tasks which I could have delegated away, but I still do them myself. If I can complete the task fairly quickly, it would have cost me much more time to tell someone what and how to do, and later check whether it was accomplished correctly. If the task does not take up too much time, it can be more efficient to not delegate it.
– ValMar 5 '15 at 22:27

I completely agree: I lead a small team (10 people) myself, and I believe in leading by example, and that sometime it is just faster to do something myself instead of delegating, but never to the point that doing hinders the ability of managing. I will edit my answer to be more precise
– Lorenzo DemattéMar 6 '15 at 6:57

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Does it impact their management ("less time to manage" doesn't mean "bad management")? Or the quality of your products? As I read the question, it seems that it has effect only on their productivity. Is there any possibility that doing lower-rank tasks is their way to make a break? Instead of going for a cigaret or checking their FaceBook wall?
– TaladrisMar 6 '15 at 7:25

Well, the productivity of a manager influences that of people below him.. if they have to wait for a decision, blocked. Or worse, wasting time in the wrong direction. And making the team's work visible: that is totally lacking
– Lorenzo DemattéMar 6 '15 at 7:28

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Getting direction, priorities, forcing decisions, timely responses is a generic issue in "managing your manager" - regardless of how exactly they're misspending their time - and has well-known generic solutions. Don't attack the symptom, attack the root-cause of the indecision: one-on-ones, standup meetings, short emails requiring a closed-form response "Should I work on task A or B?" or even stating your default action "I will do A as we agreed at least meeting unless you want to change my assigned task". Whatever communication style they seem to be most comfortable working with.
– smciMar 6 '15 at 7:36

I had many conversations about this very subject, to the point where I (and others on my team) were told to effectively "just worry about your own position and not what others were doing." Well, our main problem was that my manager was not effectively leading the team and the key obstacle to our project being successful was in fact our manager not doing the leadership/managerial duties.

Your concerns are absolutely valid.

Some things to keep in mind:

Some people are managers because of circumstance, rather than desire/ability. Many a manager gets there because they happen to be the most senior individual contributor even though they may be considerably more effective as an individual contributor than manager. Or other reasons unrelated to their ability to manage.

Some managers never accept the idea that they are managers and not worker bees.

Management offers considerably more ambiguous "what did I do at work today?" answers. For many people who like checklists and feeling accomplished, this can make work very hollow/meaningless

Management is a huge step outside a comfort zone for many people. The longer someone has been an individual contributor, the more difficult it can be.

They might be totally aware of this issue but having a really hard time doing anything about it.

This becomes more important the larger a team is. If your boss has 3 direct reports, it's less important. But if you have a team of 10, your manager doing day-to-day work is considerably more problematic.

What can you do about it?

Don't focus on the things you can't change (ie your manager's tendency to do work he shouldn't do).

Focus on what your manager is not doing for you and your team. Are you not getting the resources you need from him? Is your team not working together effectively? Do you need a team meeting/etc?

If you don't have regular 1/1s because of your manager is too busy doing day-to-day work, don't say "you should stop doing day to day work so we can have 1/1s" but just approach it from the "can we have 1/1s? this would be helpful for x/y/z reasons."

If your team needs more visibility, approach it from the perspective of, "hey, what do you think we can do to get our team more visibility?"

In addition to this, be sure to thank your manager for the effective managerial work that he does. People respond surprisingly well to positive feedback. Continually reinforcing your manager for managing is a easy, non-threatening way you can encourage them to manage rather than do day-to-day work.

"Focus on what your manager is not doing for you and your team." Great advice. The manager can do things you can't, so mention that you need them, especially if you can cite technical reasons or roadblocks (which it sounds like the manager in question will understand and want to fix). That will necessarily take time away from doing the grunt work while still offering the manager some satisfaction about solving technical issues.
– Esoteric Screen NameMar 6 '15 at 4:07

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Great advice, and you nailed the problem! I am not so concerned about him doing daily chores (even if this influences the work of my team, but that's another problem), but in him not doing managerial duties.
– Lorenzo DemattéMar 6 '15 at 6:51

Build trust. Gently explain that other are dedicated to the type of problems that they are trying to solve and offer to be a proxy (i.e. tell them that you want to help them save time and point them in the right direction whenever they have a problem like the ones above). Also gently explain that their time is super valuable and if they spend it doing things that low level drones can and are already doing you (i.e. the company) are losing money.

I'm kind of latching on to one idea that may not actually be relevant, but one thing you mentioned was the difficulty of giving up "getting my hands dirty". This could be true, or it could be that he just fails at delegating tasks once in a while. Various reasons could be at play for not delegating:

He's uncomfortable with delegating tasks(or otherwise hasn't gotten used to it yet)

The tasks he ends up doing are close to his experience, so he sees himself as the obvious candidate

He really does like getting his hands dirty.

Doing those tasks reminds him of what he's passionate about.

He wants a break from his other duties.

Etc. He certainly isn't the first person to move up and miss doing the grunt work.

If you end up in meetings where your boss says things like "Today I'm going to try doing <drone work tasks> to help you guys along", then whoever has the most experience with those drone tasks could speak up and ask to do them instead. 'Ask' is the key word in the last sentence. Don't tell your boss you're going to do the task - ask him. It's important that he sees he has the power to make the decision. Eg. (You say) "Oh! I've been working on the SQL queries lately and have a few scripts that help me. I could do <the thing> and have the report in your e-mail by close-of-business today. Would that be ok with you?"

The key is to make it really easy for him to say 'yes' to you - stack the odds in your favor however you can(you're not busy, it'll take you no time at all, you have the tools ready to go, you won't miss your deadline(s) for anything, his time is better spent elsewhere, etc).

By taking initiative to do these tasks, you(as a team) show him you're willing to step up for him to get the job done, and it's a way of easing him into delegating tasks to people. He may be good at delegating big-picture stuff. He's not stupid enough to think he can do all the work himself. But these one-off situations are trickier, especially when you remember being able to do these kinds of things in a few hours.

Personal anecdote(I've made my point by now, the rest is fluff):

I'm a very non-confrontational person and I'm also a junior software developer. I was given the reins of one of our R&D labs, which may sound more grandiose than it really was - I 'managed' 2 people's time in the lab(both working part time usually, sometimes full time) for roughly 4 months.

At the start most of my time, roughly 80% weekly, was on my main project, so I had ~8 hours per week (2 hours per day Mon-Thurs) to deal with the R&D lab. I wasn't comfortable with telling people what to do, but I really had no other choice. If I hadn't been thrown in the deep end and had to 'figure it out' so abruptly with the time constraints that I had, I think the transition would've been tougher and I'd be more prone to helping with tasks. To say the least, it was very difficult to not stick my hands in the code.

It also helped that the people I 'managed' were two coworkers I had worked with extensively who were both smart and trustworthy. When I gave them tasks, I was certain they'd ask questions if they got stuck, but otherwise they would finish them and not waste time.

Your post doesn't give too much detail, but the delegation thing just got stuck in my head since I went through that last year. If your boss is a newly-made/recently-promoted boss, perhaps that's what he's going through.

It isn't your place to do anything about this. Your manager will manage his time according to his boss and himself. If it's not affecting you then you shouldn't say anything.

If it is affecting you, for example he hasn't made a decision on which way a project should go, politely ask him for a decision and state that your work is being held up by the lack of a decision. If his queries are impacting on your work then you should point out to him how it is impacting and the right tools / libraries to use to avoid impacting on you in the future, focus on the way for him to stop impacting your work and you might just find he realises he's a bit out of touch and stops on his own. However if he wants to run those queries rather than delegate then that's his right as the Manager.

If it's such a big problem then find another job (and mention why you're leaving in your exit interview), or find a way to become a manager on the same level as him (if that's possible) and then you can talk to him as a colleague rather than your boss.

If your manager doesn't have time to manage you, it is your problem. It's important to be respectful and handle it with tact, but it's not out of "place".
– user8365Mar 6 '15 at 13:01

@JeffO You don't get to decide how your manager spends his time. If you feel he's not giving you enough time then say that, but you don't tell him to give you more time. It's not your job (i.e. not your place) to tell your manager how to do his job. If one of my staff ever came up to me and told me I wasn't managing them properly, that I needed to spend less time coding and more time on them I'd put them in their place and I wouldn't be gentle about it.
– StyphonMar 6 '15 at 13:24

I never indicated I tell my boss how to do his job, but that doesn't mean I don't provide critical feedback. He encourages it because he knows that it's more important to make informed decisions instead of acting like a bully with an inferiority complex.
– user8365Mar 19 '15 at 18:24

I have had directors & managers from both sides of the competence scale in regards to being able to perform the work of the people under them. You will find that in some cases while they may appear 'slower' than you or your peers they are checking up on the quality of other work, if they are on the lower end of the competence scale they may be simply doing it as exercises to familiarize themselves with day to day operations or trying to figure out where bottlenecks are. ( remember at Mcdonalds a manager is someone who knows every single job in the store inside and out. )

Now if its a director that is doing this you have to be aware that "its their company", you just happen to be there because it suits them to have you around. They were there long before you started and will be there long after you leave. and more likely than not when the company first started it was them that did the lions share of the work, and as time progressed more and more staff got added because their workload increased.

EDIT: this answer as written when OP's original version implied they were an individual contributor, before the crucial detail that they are a manager managing a team of 10, which completely changes the question.
Moreover this makes the boss a level-2 manager, which is a different situation.

I'd bloody rejoice.

A manager who wants to keep their hand in the game? Consider yourself lucky. This is a blessing in disguise.

I don't see that this a problem, certainly no more than a manager who spends too much time in meetings, presentations, reviews, conferences, executive lunches, politicking, MBA classes, playing golf, drinking, betting on the horses or other sanctioned modes of slacking.

Even if we conclude it's a problem, it's at most a small problem and it's certainly not your problem.
One good side-effect is that they will still be competent at hiring good technical people, which is something that PowerPoint warriors lose (or delegate to the HR dept, or stop caring, and the organizational rot sets in).

(What's their motivation? Need to present credible data to higher-ups? Want to stay technical and deny the cloak of management being thrust upon them? Technically insecure? Impostor syndrome? Afraid of being laid off, or that their role has become obsolete? Want to understand what you or their subordinates are doing better? Want to know how to hire or manage you better? or hire your replacement if you leave? They may have several of these motivations, and don't expect them to tell you.)
Most of those are fine, and even the ones that aren't can work to your advantage.

You can (privately) show them you that you can do their work faster (or some automated script, or query tool, or GUI).
Implement it yourself. If they're a chart person, give them charts. If they're a KPI person, give them numbers. If they like doing it interactively, install a query tool and write a wiki of frequently-used queries. If they want to tie things to the build/SCM process, implement that.
Consider this a hidden opportunity to both do something productive and "get recognition" at multiple levels of the hierarchy.
This is how useful internal tools generally happen. Show them a functional prototype then see if they approve spending further time on it.
a

I know that for some people giving up the "getting my hands dirty" is difficult

Honestly that's a badge of being a good engineer, if somewhat unrealistic about their productivity. (Read about "Engineer-not-Manager")

How can I convince them to stop "doing", without being rude, annoying, or worse?

It's not your %#@& job to. If you must, be very oblique. Just offer them a higher-productivity alternative, and privately walk them through it, only if they show interest. Then if they still insist on doing it themselves, then let it be.
They may have some unresolved identity or competence crisis; if so, don't force it.

but I really feel this is becoming a problem and I want to try to improve the situation.

But it's not, based on anything you've said! Anyway it's not your perception that matters as to whether it's a problem. Don't let your ego be threatened, don't feel insecure.

tl;dr: Rejoice, let it go, use it to your career advantage, keep them happy while nudging them towards a mutually useful point, boost their managerial self-esteem

This is completely dependent on the effectiveness and efficiency of the manager's work. I've had fantastic managers who fit your description and really help the team, but also ones who say "you have no idea what you're talking about, I've been doing this for 20 years!" and then implement a bunch of cron jobs requiring manual daily maintenance when a two line built in API call would fix the entire problem. Tough to say where on the spectrum the OP's manager lies.
– Esoteric Screen NameMar 6 '15 at 3:16

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You have obviously never had a manager who was so caught up in day-to-day work that they were ineffective as a manager... it absolutely becomes your problem if your manager neglects managerial duties for the sake of doing day-to-day work.
– enderlandMar 6 '15 at 3:33

@EsotericScreenName , enderland : the OP's question specifically makes it clear their manager isn't "so caught up... as to be ineffective". This isn't your question, it's his(/her) question. Don't downvote this for your experiences, which are not at issue in this question. Ask a separate question. Also, you're wrong in speculating I haven't had a manager who was ineffective for related reasons. But we can't hijack the OP's question with a different question.
– smciMar 6 '15 at 3:42

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@smci from the question - I really feel this is becoming a problem and I want to try to improve the situation
– enderlandMar 6 '15 at 3:47

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@smci "This is not a very urgent problem... but that eats up their time, and that's the real issue: he does have very little time to "manage"" I take this to mean that the manager's technical work isn't bad (but could be better) but that management duties aren't getting done because time is being spent on technical issues.
– Esoteric Screen NameMar 6 '15 at 3:48